module Math
  def Math::pow(n, e)
    n ** e
  end
end

module LatLongUTM
  
  SM_A = 6378137.0
  SM_B = 6356752.314
  UTMScaleFactor = 0.9996
  
  def LatLongUTM::DegToRad(deg)
    return (deg / 180.0 * Math::PI)
  end

  def LatLongUTM::RadToDeg(rad)
      return (rad / Math::PI * 180.0)
  end
  
  # ArcLengthOfMeridian
  # Computes the ellipsoidal distance from the equator to a point at a
  # given latitude.
  # Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
  # GPS: Theory and Practice, 3rd ed.  new York: Springer-Verlag Wien, 1994.
  # Inputs:
  #     phi - Latitude of the point, in radians.
  # Globals:
  #     SM_A - Ellipsoid model major axis.
  #     SM_B - Ellipsoid model minor axis.
  # Returns:
  #     The ellipsoidal distance of the point from the equator, in meters.
  def LatLongUTM::ArcLengthOfMeridian(phi)
    n = (SM_A - SM_B) / (SM_A + SM_B)

    # Precalculate alpha
    alpha = ((SM_A + SM_B) / 2.0) \
       * (1.0 + (Math.pow(n, 2.0) / 4.0) + (Math.pow(n, 4.0) / 64.0))

    # Precalculate beta
    beta = (-3.0 * n / 2.0) + (9.0 * Math.pow(n, 3.0) / 16.0) \
       + (-3.0 * Math.pow(n, 5.0) / 32.0)

    # Precalculate gamma 
    gamma = (15.0 * Math.pow(n, 2.0) / 16.0) \
        + (-15.0 * Math.pow(n, 4.0) / 32.0)

    # Precalculate delta
    delta = (-35.0 * Math.pow(n, 3.0) / 48.0) \
        + (105.0 * Math.pow(n, 5.0) / 256.0)

    # Precalculate epsilon 
    epsilon = (315.0 * Math.pow(n, 4.0) / 512.0)

    # now calculate the sum of the series and return 
    result = alpha \
        * (phi + (beta * Math.sin(2.0 * phi)) \
            + (gamma * Math.sin(4.0 * phi)) \
            + (delta * Math.sin(6.0 * phi)) \
            + (epsilon * Math.sin(8.0 * phi)))

    return result
  end

  # UTMCentralMeridian
  # Determines the central meridian for the given UTM zone.
  # Inputs:
  #     zone - An integer value designating the UTM zone, range [1,60].
  # Returns:
  #   The central meridian for the given UTM zone, in radians, or zero
  #   if the UTM zone parameter is outside the range [1,60].
  #   Range of the central meridian is the radian equivalent of [-177,+177].
  def LatLongUTM::UTMCentralMeridian(zone)
    cmeridian = DegToRad(-183.0 + (zone * 6.0))
    return cmeridian
  end

  # FootpointLatitude
  # Computes the footpoint latitude for use in converting transverse
  # Mercator coordinates to ellipsoidal coordinates.
  # Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
  #   GPS: Theory and Practice, 3rd ed.  new York: Springer-Verlag Wien, 1994.
  # Inputs:
  #   y - The UTM northing coordinate, in meters.
  # Returns:
  #   The footpoint latitude, in radians.
  def LatLongUTM::FootpointLatitude(y)
    # Precalculate n (Eq. 10.18)
    n = (SM_A - SM_B) / (SM_A + SM_B)
    
    # Precalculate alpha_ (Eq. 10.22)
    # (Same as alpha in Eq. 10.17)
    alpha_ = ((SM_A + SM_B) / 2.0) \
        * (1 + (Math.pow(n, 2.0) / 4) + (Math.pow(n, 4.0) / 64))
  
    # Precalculate y_ (Eq. 10.23)
    y_ = y / alpha_
  
    # Precalculate beta_ (Eq. 10.22)
    beta_ = (3.0 * n / 2.0) + (-27.0 * Math.pow(n, 3.0) / 32.0) \
        + (269.0 * Math.pow(n, 5.0) / 512.0)
  
    # Precalculate gamma_ (Eq. 10.22)
    gamma_ = (21.0 * Math.pow(n, 2.0) / 16.0) \
        + (-55.0 * Math.pow(n, 4.0) / 32.0)

    # Precalculate delta_ (Eq. 10.22)
    delta_ = (151.0 * Math.pow(n, 3.0) / 96.0) \
        + (-417.0 * Math.pow(n, 5.0) / 128.0)
    
    # Precalculate epsilon_ (Eq. 10.22)
    epsilon_ = (1097.0 * Math.pow(n, 4.0) / 512.0)
    
    # now calculate the sum of the series (Eq. 10.21)
    result = y_ + (beta_ * Math.sin(2.0 * y_)) \
        + (gamma_ * Math.sin(4.0 * y_)) \
        + (delta_ * Math.sin(6.0 * y_)) \
        + (epsilon_ * Math.sin(8.0 * y_))
  
    return result
  end

  # MapLatLonToXY
  # Converts a latitude/longitude pair to x and y coordinates in the
  # Transverse Mercator projection.  note that Transverse Mercator is not
  # the same as UTM; a scale factor is required to convert between them.
  # Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
  # GPS: Theory and Practice, 3rd ed.  new York: Springer-Verlag Wien, 1994.
  # Inputs:
  #    phi - Latitude of the point, in radians.
  #    lambda - Longitude of the point, in radians.
  #    lambda0 - Longitude of the central meridian to be used, in radians.
  # Returns:
  #    A 2-element array containing the x and y coordinates
  #         of the computed point.
  def LatLongUTM::MapLatLonToXY(phi, lambda, lambda0)

    # Precalculate ep2
    ep2 = (Math.pow(SM_A, 2.0) - Math.pow(SM_B, 2.0)) / Math.pow(SM_B, 2.0)

    # Precalculate nu2
    nu2 = ep2 * Math.pow(Math.cos(phi), 2.0)

    # Precalculate n
    n = Math.pow(SM_A, 2.0) / (SM_B * Math.sqrt(1 + nu2))

    # Precalculate t
    t = Math.tan(phi)
    t2 = t * t
    tmp = (t2 * t2 * t2) - Math.pow(t, 6.0)

    # Precalculate l
    l = lambda - lambda0

    # Precalculate coefficients for l**n in the equations below
    #   so a normal human being can read the expressions for easting
    #   and northing
    #   -- l**1 and l**2 have coefficients of 1.0
    l3coef = 1.0 - t2 + nu2

    l4coef = 5.0 - t2 + 9 * nu2 + 4.0 * (nu2 * nu2)

    l5coef = 5.0 - 18.0 * t2 + (t2 * t2) + 14.0 * nu2 \
        - 58.0 * t2 * nu2

    l6coef = 61.0 - 58.0 * t2 + (t2 * t2) + 270.0 * nu2 \
        - 330.0 * t2 * nu2

    l7coef = 61.0 - 479.0 * t2 + 179.0 * (t2 * t2) - (t2 * t2 * t2)

    l8coef = 1385.0 - 3111.0 * t2 + 543.0 * (t2 * t2) - (t2 * t2 * t2)

    xy = []
    # Calculate easting (x)
    xy[0] = n * Math.cos(phi) * l \
        + (n / 6.0 * Math.pow(Math.cos(phi), 3.0) * l3coef * Math.pow(l, 3.0)) \
        + (n / 120.0 * Math.pow(Math.cos(phi), 5.0) * l5coef * Math.pow(l, 5.0)) \
        + (n / 5040.0 * Math.pow(Math.cos(phi), 7.0) * l7coef * Math.pow(l, 7.0))

    # Calculate northing (y)
    xy[1] = ArcLengthOfMeridian(phi) \
        + (t / 2.0 * n * Math.pow(Math.cos(phi), 2.0) * Math.pow(l, 2.0)) \
        + (t / 24.0 * n * Math.pow(Math.cos(phi), 4.0) * l4coef * Math.pow(l, 4.0)) \
        + (t / 720.0 * n * Math.pow(Math.cos(phi), 6.0) * l6coef * Math.pow(l, 6.0)) \
        + (t / 40320.0 * n * Math.pow(Math.cos(phi), 8.0) * l8coef * Math.pow(l, 8.0))
        
    return xy
  end

  # MapXYToLatLon
  # Converts x and y coordinates in the Transverse Mercator projection to
  # a latitude/longitude pair.  note that Transverse Mercator is not
  # the same as UTM; a scale factor is required to convert between them.
  # Reference: Hoffmann-Wellenhof, B., Lichtenegger, H., and Collins, J.,
  #   GPS: Theory and Practice, 3rd ed.  new York: Springer-Verlag Wien, 1994.
  # Inputs:
  #   x - The easting of the point, in meters.
  #   y - The northing of the point, in meters.
  #   lambda0 - Longitude of the central meridian to be used, in radians.
  # Returns:
  #   philambda - A 2-element containing the latitude and longitude
  #               in radians.
  # Remarks:
  #   The local variables nf, nuf2, tf, and tf2 serve the same purpose as
  #   n, nu2, t, and t2 in MapLatLonToXY, but they are computed with respect
  #   to the footpoint latitude phif.
  #   x1frac, x2frac, x2poly, x3poly, etc. are to enhance readability and
  #   to optimize computations.
  def LatLongUTM::MapXYToLatLon(x, y, lambda0)
    # Get the value of phif, the footpoint latitude.
    phif = FootpointLatitude(y)
    
    # Precalculate ep2
    ep2 = (Math.pow(SM_A, 2.0) - Math.pow(SM_B, 2.0)) / Math.pow(SM_B, 2.0)
    
    # Precalculate cos (phif)
    cf = Math.cos(phif)
    
    # Precalculate nuf2
    nuf2 = ep2 * Math.pow(cf, 2.0)
    
    # Precalculate nf and initialize nfpow 
    nf = Math.pow(SM_A, 2.0) / (SM_B * Math.sqrt(1 + nuf2))
    nfpow = nf
    
    # Precalculate tf
    tf = Math.tan(phif)
    tf2 = tf * tf
    tf4 = tf2 * tf2
  
    # Precalculate fractional coefficients for x**n in the equations
    # below to simplify the expressions for latitude and longitude.
    x1frac = 1.0 / (nfpow * cf)
  
    nfpow *= nf   # now equals nf**2)
    x2frac = tf / (2.0 * nfpow)
  
    nfpow *= nf   # now equals nf**3)
    x3frac = 1.0 / (6.0 * nfpow * cf)
  
    nfpow *= nf;   # now equals nf**4) 
    x4frac = tf / (24.0 * nfpow)
  
    nfpow *= nf;   # now equals nf**5)
    x5frac = 1.0 / (120.0 * nfpow * cf)
  
    nfpow *= nf;   # now equals nf**6)
    x6frac = tf / (720.0 * nfpow)
  
    nfpow *= nf;   # now equals nf**7)
    x7frac = 1.0 / (5040.0 * nfpow * cf)
  
    nfpow *= nf;   # now equals nf**8)
    x8frac = tf / (40320.0 * nfpow)
  
    # Precalculate polynomial coefficients for x**n.
    #  -- x**1 does not have a polynomial coefficient.
    x2poly = -1.0 - nuf2
  
    x3poly = -1.0 - 2 * tf2 - nuf2
  
    x4poly = 5.0 + 3.0 * tf2 + 6.0 * nuf2 - 6.0 * tf2 * nuf2 \
      - 3.0 * (nuf2 *nuf2) - 9.0 * tf2 * (nuf2 * nuf2)
  
    x5poly = 5.0 + 28.0 * tf2 + 24.0 * tf4 + 6.0 * nuf2 + 8.0 * tf2 * nuf2
  
    x6poly = -61.0 - 90.0 * tf2 - 45.0 * tf4 - 107.0 * nuf2 \
      + 162.0 * tf2 * nuf2
  
    x7poly = -61.0 - 662.0 * tf2 - 1320.0 * tf4 - 720.0 * (tf4 * tf2)
  
    x8poly = 1385.0 + 3633.0 * tf2 + 4095.0 * tf4 + 1575 * (tf4 * tf2)

    philambda = []
    # Calculate latitude
    philambda[0] = phif + x2frac * x2poly * (x * x) \
      + x4frac * x4poly * Math.pow(x, 4.0) \
      + x6frac * x6poly * Math.pow(x, 6.0) \
      + x8frac * x8poly * Math.pow(x, 8.0)
    
    # Calculate longitude
    philambda[1] = lambda0 + x1frac * x \
      + x3frac * x3poly * Math.pow(x, 3.0) \
      + x5frac * x5poly * Math.pow(x, 5.0) \
      + x7frac * x7poly * Math.pow(x, 7.0)
    
    return philambda
  end

  # LatLonToUTMXY
  # Converts a latitude/longitude pair to x and y coordinates in the
  # Universal Transverse Mercator projection.
  # Inputs:
  #   lat - Latitude of the point, in radians.
  #   lon - Longitude of the point, in radians.
  #   zone - UTM zone to be used for calculating values for x and y.
  #          If zone is less than 1 or greater than 60, the routine
  #          will determine the appropriate zone from the value of lon.
  # Outputs:
  #   xy - A 2-element array where the UTM x and y values will be stored.
  # Returns:
  #   The UTM zone used for calculating the values of x and y.
  def LatLongUTM::LatLonToUTMXY(lat, lon, zone, xy)
      MapLatLonToXY(lat, lon, UTMCentralMeridian(zone), xy)

      # Adjust easting and northing for UTM system.
      xy[0] = xy[0] * UTMScaleFactor + 500000.0
      xy[1] = xy[1] * UTMScaleFactor
      if (xy[1] < 0.0)
          xy[1] = xy[1] + 10000000.0
      end
      return zone
  end


  # UTMXYToLatLon
  # Converts x and y coordinates in the Universal Transverse Mercator
  # projection to a latitude/longitude pair.
  # x - The easting of the point, in meters.
  # y - The northing of the point, in meters.
  # zone - The UTM zone in which the point lies.
  # southhemi - True if the point is in the southern hemisphere;
  #               false otherwise.
  # Outputs:
  # latlon - A 2-element array containing the latitude and
  #            longitude of the point, in radians.
  # Returns:
  # The function does not return a value.
  def LatLongUTM::UTMXYToLatLon(x, y, zone, southhemi)
      
    x -= 500000.0
    x /= UTMScaleFactor
    
    # If in southern hemisphere, adjust y accordingly.
    if (southhemi)
      y -= 10000000.0
    end
      
    y /= UTMScaleFactor
  
    cmeridian = UTMCentralMeridian(zone)
    return MapXYToLatLon(x, y, cmeridian)
  end
end